Geometric structures on orbifolds and holonomy representations

Details Geometric structures on orbifolds and holonomy representations Geometric structures on orbifolds and holonomy representations

2001-07-24

arxiv.org/abs/math/0107172v2

Mathematics

Geometric Topology

35 pages

Scientific paper

An orbifold is a topological space modeled on quotient spaces of a finite group actions. We can define the universal cover of an orbifold and the fundamental group as the deck transformation group. Let $G$ be a Lie group acting on a space $X$. We show that the space of isotopy-equivalence classes of $(G,X)$-structures on a compact orbifold $\Sigma$ is locally homeomorphic to the space of representations of the orbifold fundamental group of $\Sigma$ to $G$ following the work of Thurston, Morgan, and Lok. This implies that the deformation space of $(G, X)$-structures on $\Sigma$ is locally homeomorphic to the space of representations of the orbifold fundamental group to $G$ when restricted to the region of proper conjugation action by $G$.

Affiliated with

Also associated with

No associations

Rating

Geometric structures on orbifolds and holonomy representations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric structures on orbifolds and holonomy representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric structures on orbifolds and holonomy representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-322742